Problem: Simplify the following expression: $ r = \dfrac{7}{10} + \dfrac{p + 1}{-6p} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6p}{-6p}$ $ \dfrac{7}{10} \times \dfrac{-6p}{-6p} = \dfrac{-42p}{-60p} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{p + 1}{-6p} \times \dfrac{10}{10} = \dfrac{10p + 10}{-60p} $ Therefore $ r = \dfrac{-42p}{-60p} + \dfrac{10p + 10}{-60p} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-42p + 10p + 10}{-60p} $ $r = \dfrac{-32p + 10}{-60p}$ Simplify the expression by dividing the numerator and denominator by -2: $r = \dfrac{16p - 5}{30p}$